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CONSTRUCTION OF CUBATURE FORMULAS VIA BIVARIATE QUADRATIC SPLINE SPACES OVER NON-UNIFORM TYPE-2 TRIANGULATION

Journal of Computational Mathematics 2022年第2期40卷 205-230页

作者： Jiang Qian Xiquan Shi Jinming Wu Dianxuan Gong College of Science Hohai UniversityNanjing 211100China Key Laboratory of Coastal Disaster and Defence(Hohai University) Ministry of EducationNanjing 210098China Division of Physics EngineeringMathematicsand Computer ScienceDelaware State UniversityDoverDE 19901USA Statistics and Mathematics Institute Zhejiang Gongshang UniversityHangzhou 310018China College of Science North China University of Science and TechnologyTangshan 063210China

In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated ***,by means of coefficients in terms of B-net,computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of *** concise bivariate cubature formulas are constructed over rectangular ***,by means of module of continuity and max-norms,error estimates for cubature formulas are derived over both sub-domains and the domain.

关键词： Multivariate spline Bivariate cubature conformality of smoothing cofactor method B-net Non-uniform Type-2 Triangulation

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On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline Space S_(3)^(1,2)(∆_(mn)^((2)))

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Numerical Mathematics(Theory,methods and Applications) 2014年第1期7卷 1-22页

作者： Jiang Qian Fan Wang College of Sciences Hohai UniversityNanjing 210098China Center for Numerical Simulation Software in Engineering and Sciences Department of Engineering MechanicsHohai UniversityNanjing 210098China College of Engineering Nanjing Agricultural UniversityNanjing 210031China

In this paper,based on the basis composed of two sets of splines with distinct local supports,cubic spline quasi-interpolating operators are reviewed on nonuniform type-2 *** variation diminishing operator is defined by discrete linear functionals based on a fixed number of triangular mesh-points,which can reproduce any polynomial of nearly best *** by means of the modulus of continuity,the estimation of the operator approximating a real sufficiently smooth function is reviewed as ***,the derivatives of the nearly optimal variation diminishing operator can approximate that of the real sufficiently smooth function uniformly over quasi-uniform type-2 *** then the convergence results are worked out.

关键词： Bivariate splines conformality of smoothing cofactor method nonuniform type-2 triangulation quasi-interpolation modulus of continuity

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The Bases of the Non-Uniform Cubic Spline Space S_(3)^(1,2)(Δ_(mn)^((2))

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Numerical Mathematics(Theory,methods and Applications) 2012年第4期5卷 635-652页

作者： Jiang Qian Renhong Wang Chongjun Li College of Sciences Hohai UniversityNanjing 210098China School of Mathematical Sciences Dalian University of TechnologyDalian 116024China

In this paper,the dimension of the nonuniform bivariate spline space S_(3)^(1,2)(Δ_(mn)^((2))is discussed based on the theory of multivariate spline ***,by means of the conformality of smoothing cofactor method,the basis ofS_(3)^(1,2)(Δ_(mn)^((2))composed of two sets of splines are worked out in the form of the values at ten domain points in each triangular cell,both of which possess distinct local ***,the explicit coefficients in terms of B-net are obtained for the two sets of splines respectively.

关键词： Bivariate spline conformality of smoothing cofactor method B-net nonuniform type-2 triangulation

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